Vol. 15, No. 4, 1965

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Invariant splitting in Jordan and alternative algebras

Earl J. Taft

Vol. 15 (1965), No. 4, 1421–1427

Let A be a finite-dimensional Jordan or alternative algebra over a field F of characteristic 0. Let N denote the radical of A. Then A possesses maximal semisimple subalgebras isomorphic to A∕N, [5], [6], any two of which are strictly conjugate, [2], [9]. If G is a finite group of automorphisms and antiautomorphisms of A, then A possesses G-invariant maximal semisimple subalgebras, [10]. We investigate here the uniqueness question for such G-invariant maximal semisimple subalgebras. The result is that the strict conjugacy can be chosen to commute pointwise with G and to be in the enveloping associative algebra generated by the right and left multiplications in A.

Mathematical Subject Classification
Primary: 17.40
Secondary: 17.50
Received: 15 July 1964
Published: 1 December 1965
Earl J. Taft